Understanding Standard Deviation Visually

Standard deviation is a value that shows, on average, how far the data are from the mean.

For example, if asset A's monthly return is almost constant at +1% every month, there's almost no scatter, so the standard deviation is small. Conversely, if asset B swings widely—+15% one month, -12% another—the scatter is large, so the standard deviation is large.

So in investing, a large standard deviation means 'the returns jump around,' i.e., high volatility. It's a ruler that measures not the size of the return but the size of the 'swings.'

If you assume returns follow a bell shape (a normal distribution), standard deviation lets you say 'how often they stay within which range.'

- About 68% within the mean ±1 standard deviation - About 95% within the mean ±2 standard deviations - About 99.7% within the mean ±3 standard deviations

For example, for a stock with an annual average return of 8% and an annual standard deviation of 15%, roughly two-thirds of years fall between -7% and +23%. The remaining third falls outside that. In this way, standard deviation sketches out the 'range of common outcomes.'

Standard deviation counts a swing upward (a surge) and a swing downward (a plunge) equally as 'variation.' So a big rise is also captured as 'risk.'

But what truly scares investors is the downside. To make up for this limitation, measures emerged that count only downward swings—downside deviation, and the Sortino ratio that uses it.

Standard deviation is the most basic and widely used, but remember that it cannot distinguish the 'direction of the swings,' and it's best viewed together with the maximum drawdown (MDD).